The colored Jones polynomial of singular knots

被引：0

作者：

Bataineh, Khaled ^{[1
]}

Elhamdadi, Mohamed ^{[2
]}

Hajij, Mustafa ^{[2
]}

机构：

[1] Jordan Univ Sci & Technol, Dept Math & Stat, Irbid 22110, Jordan

[2] Univ S Florida, Dept Math, Tampa, FL 33647 USA

来源：

NEW YORK JOURNAL OF MATHEMATICS | 2016年 / 22卷

关键词：

Skein theory; singular knots; colored Jones polynomial; QUANTUM GROUPS; KAUFFMAN BRACKET; INVARIANTS; 3-MANIFOLDS; GRAPHS; LINKS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We generalize the colored Jones polynomial to 4-valent graphs. This generalization is given as a sequence of invariants in which the first term is a one variable specialization of the Kauffman-Vogel polynomial. We use the invariant we construct to give a sequence of singular braid group representations.

引用

页码：1439 / 1456

页数：18

共 50 条

[1] FOUNDATIONS OF THE COLORED JONES POLYNOMIAL OF SINGULAR KNOTS
Elhamdadi, Mohamed
Hajij, Mustafa
[J]. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2018, 55 (03) : 937 - 956
[2] The colored Jones polynomial and the A-polynomial of knots
Le, Thang T. Q.
[J]. ADVANCES IN MATHEMATICS, 2006, 207 (02) : 782 - 804
[3] THE HEAD AND TAIL OF THE COLORED JONES POLYNOMIAL FOR ADEQUATE KNOTS
Armond, Cody
Dasbach, Oliver T.
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (03) : 1357 - 1367
[4] THE COLORED JONES FUNCTION AND ALEXANDER POLYNOMIAL FOR TORUS KNOTS
MORTON, HR
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1995, 117 : 129 - 135
[5] On the asymptotic expansion of the colored Jones polynomial for torus knots
Jérôme Dubois
Rinat Kashaev
[J]. Mathematische Annalen, 2007, 339 : 757 - 782
[6] On the asymptotic expansion of the colored Jones polynomial for torus knots
Dubois, Jerome
Kashaev, Rinat
[J]. MATHEMATISCHE ANNALEN, 2007, 339 (04) : 757 - 782
[7] A Formula for the Colored Jones Polynomial of 2-Bridge Knots
Takata, Toshie
[J]. KYUNGPOOK MATHEMATICAL JOURNAL, 2008, 48 (02): : 255 - 280
[8] ON THE 2-HEAD OF THE COLORED JONES POLYNOMIAL FOR PRETZEL KNOTS
Beirne, Paul
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 2019, 70 (04): : 1353 - 1370
[9] The colored Jones polynomial and Kontsevich-Zagier series for double twist knots
Lovejoy, Jeremy
Osburn, Robert
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2021, 30 (05)
[10] On the Jones polynomial of ribbon knots
Tanaka, T
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2005, 14 (01) : 1 - 2

← 1 2 3 4 5 →